Trajectory-Protected Quantum Computing

TL;DR

A quantum computing model that utilizes a qubit's motion to protect it from decoherence and the fundamental limits on quantum error protection are discussed, comparable to the Eastin-Knill theorem for quantum error correction.

Abstract

We introduce a novel method that simultaneously isolates a quantum computer from decoherence and enables the controlled implementation of computational gates. We demonstrate a quantum computing model that utilizes a qubit's motion to protect it from decoherence. We model a qubit interacting with a quantum field via the standard light-matter interaction model: an Unruh-DeWitt detector, i.e., the qubit, follows a prescribed classical trajectory while interacting with a scalar quantum field. We switch off the rotating-wave terms, i.e., the resonant transitions, using the technique of acceleration-induced transparency which eliminates the dominant decoherence channels by controlling the qubit's trajectory. We are able to perform one-qubit gates by stimulating the counter-rotating wave terms (i.e., the non-resonant transitions) and two-qubit gates by extracting the entanglement from the quantum field prepared in a squeezed state. Finally, we discuss the fundamental limits on quantum error protection: on the trade-off between isolating a quantum computer from decoherence, and the speed with which entangling gates may be applied, comparable to the Eastin-Knill theorem for quantum error correction.

Figures (3)

• Figure 1: A schematic depiction of our quantum computing setup: qubits are placed in trajectories, and they are following prescribed, externally controlled trajectories. We can also control the state of the quantum field in its cavity environment by producing a coherent state, represented here schematically by shining a laser onto the right qubit's cavity, or a squeezed state.
• Figure 2: Plot of a trajectory that satisfies both transparency and periodicity constraints. It consists of a concatenation of inertial trajectories with different velocities, e.g. $v_c = 0.66,v'_c=0.46$, and the rest are explained in Supplementary Information.
• Figure 3: The negativity acquired by the two-qubit system as a function of the squeezing parameter $r$ for the optimal value of $\varphi$ for a fixed $\Omega$ and $\bm k$, when the qubit undergoes a transparent trajectory.